Question: Simplify the expression. $(3t^{2}+2t)(t^{4}+t^{3}-7t)$
Answer: First use the distributive property. $ 3 t^2 ( t^4) + 3 t^2 ( t^3) + 3 t^2 (-7 t) + 2 t ( t^4) + 2 t ( t^3) + 2 t (-7 t) $ Simplify. $ 3t^{6} + 3t^{5} - 21t^{3} + 2t^{5} + 2t^{4} - 14t^{2} $ $3t^{6}+5t^{5}+2t^{4}-21t^{3}-14t^{2}$ Identify like terms. $ { 3t^{6}} {+ 3t^{5}} {- 21t^{3}} {+ 2t^{5}} {+ 2t^{4}} {- 14t^{2}} $ Add the coefficients. $ { 3t^{6}} {+ 5t^{5}} {+ 2t^{4}} { -21t^{3}} { -14t^{2}} $